In this note, we show that the holonomy group of a Riemannian connection on a k-dimensional Euclidean vector bundle is transitive on the unit sphere bundle whenever the Euler class χ is spherical. We extract several consequences from this, among them that this is always the case as long as χ does not vanish, and the base of the bundle is simply connected and rationally (k + 1)/2-connected.

Using covering graph techniques, a structural result about connected cubic simple graphs admitting an edge-transitive solvable group of automorphisms is proved. This implies, among other, that every such graph can be obtained from either the 3-dipole Dip3 or the complete graph K4, by a sequence of elementary-abelian covers. Another consequence of the main structural result is that the action of...

This progress report surveys some of my scientiic work on part A of the Ph.D.-programme at the Computer Science Department of the University of Aarhus. I give a survey-like introduction to the eld of Complexity Theory to which my results bear relevance. I give a general account of my contributions to the eld, including the the Dynamic Transitive Closure Problem for spherical st-graphs, the Dyna...

Abstract We determine all finite sets of equiangular lines spanning finite-dimensional complex unitary spaces for which the action on set-stabiliser in group is 2-transitive with a regular normal subgroup.

We establish a set of general results to study how the Galois action on modular tensor categories interacts with fusion subcategories. This includes characterization subcategories which are closed under action, and classification factor as product pointed transitive in terms pseudoinvertible objects. As an application, we classify two orbits simple objects nontrivial grading group.

In a non-complete graph $Gamma$, a vertex triple $(u,v,w)$ with $v$ adjacent to both $u$ and $w$ is called a $2$-geodesic if $uneq w$ and $u,w$ are not adjacent. The graph $Gamma$ is said to be   $2$-geodesic transitive if its automorphism group is transitive on arcs, and also on 2-geodesics. We first produce a reduction theorem for the family of $2$-geodesic transitive graphs of prime power or...

We prove that the action of the special automorphism group on affine cones over del Pezzo surfaces of degree 4 and 5 is infinitely transitive.

This paper forms part of the general development of the theory of quasigroup permutation representations. Here, the concept of sharp transitivity is extended from group actions to quasigroup actions. Examples of nontrivial sharply transitive sets of quasigroup actions are constructed. A general theorem shows that uniformity of the action is necessary for the existence of a sharply transitive se...